Einstein's mirror

I have just recently read about the thought experiment called 'Einstein's mirror'. I understand that the imaginary experimenter loses his reflection in the mirror when he travels at the speed of light through the luminiferous aether. The loss of reflection itself is enough evidence for Einstein to reject the hypothesis of an all-pervading aether which carries electromagnetic waves. But as far as I know, the technology at that time was not sufficiently advanced to allow someone to travel even close to the speed of light. So, how could Einstein have known that he wouldn't lose his reflection were he to travel at the speed of light?

I have just recently read about the thought experiment called 'Einstein's mirror'. I understand that the imaginary experimenter loses his reflection in the mirror when he travels at the speed of light through the luminiferous aether. The loss of reflection itself is enough evidence for Einstein to reject the hypothesis of an all-pervading aether which carries electromagnetic waves. But as far as I know, the technology at that time was not sufficiently advanced to allow someone to travel even close to the speed of light. So, how could Einstein have known that he wouldn't lose his reflection were he to travel at the speed of light?